Rangers confirmed the appointment of Van Bronckhorst on Thursday, just a week after they were left shocked at the departure of Steven Gerrard to Aston Villa.
He will not be in the dugout for the Scottish League Cup semi-final clash against Hibernian on Sunday and will officially take charge of his first game as Rangers manager in the Sparta Prague game next Thursday.
Rangers are sitting at the top of the Scottish Premiership standings, but Wilson pointed at the tough run of fixtures the club will be facing ahead of the end of the year.
The former midfielder stressed that the Dutchman will need to get it right as soon as he takes charge of the side due to the difficulty of the games coming up in the next few weeks.
Wilson said on Clyde 1’s Superscoreboard: “The semi-final, okay, he won’t be in charge.
“Sparta Prague, Livingston away, and we have seen how hard that has been for the clubs, then Hibs away as well.
“You see few weeks down the line – Lyon and Hearts away.
“He has got a tough start so he has to get it right, right away.”
Rangers’ players will hope to impress Van Bronckhorst by beating Hibernian and reaching the final of the Scottish League Cup this weekend.